Random Triangle Theory with Geometry and Applications

What is the probability that a random triangle is acute? We explore this old question from a modern viewpoint, taking into account linear algebra, shape theory, numerical analysis, random matrix theory, the Hopf fibration, and much much more. One of the best distributions of random triangles takes all six vertex coordinates as independent standard Gaussians. Six can be reduced to four by translation of the center to $(0,0)$ or reformulation as a 2x2 matrix problem. In this note, we develop shape theory in its historical context for a wide audience. We hope to encourage other to look again (and differently) at triangles. We provide a new constructive proof, using the geometry of parallelians, of a central result of shape theory: Triangle shapes naturally fall on a hemisphere. We give several proofs of the key random result: that triangles are uniformly distributed when the normal distribution is transferred to the hemisphere. A new proof connects to the distribution of random condition numbers. Generalizing to higher dimensions, we obtain the "square root ellipticity statistic" of random matrix theory. Another proof connects the Hopf map to the SVD of 2 by 2 matrices. A new theorem describes three similar triangles hidden in the hemisphere. Many triangle properties are reformulated as matrix theorems, providing insight to both. This paper argues for a shift of viewpoint to the modern approaches of random matrix theory. As one example, we propose that the smallest singular value is an effective test for uniformity. New software is developed and applications are proposed

Inspection based evaluations

Usability inspection methods (UIMs) remain an important discount method for usability evaluation. They can be applied to any designed artefact during development: a paper prototype, a storyboard, a working prototype (e.g., in Macromedia Flash™ or in Microsoft PowerPoint™), tested production software, or an installed public release. They are analytical evaluation methods, which involve no typical end users, unlike empirical methods such as user testing. UIMs only require availability of a designed artefact and trained analysts. Thus, evaluation is possible with low resources (hence discount methods). Although risks arise from low resources, well-informed practices disproportionately improve analyst performance, improving cost-benefit ratios. This chapter introduces UIMs, covering six and one further method, and provides approaches to assessing existing, emerging and future UIMs and their effective uses

Falsification testing for usability inspection method assessment

We need more reliable usability inspection methods (UIMs), but assessment of UIMs has been unreliable [5]. We can only reliably improve UIMs if we have more reliable assessment. When assessing UIMs, we need to code analysts’ predictions as true or false positives or negatives, or as genuinely missed problems. Defenders of UIMs often claim that false positives cannot be accurately coded, i.e., that a prediction is true but has never shown up through user testing or other validation approaches. We show this and similar claims to be mistaken by briefly reviewing methods for reliable coding of each of five types of prediction outcome. We focus on falsification testing, which allows confident coding of false positives

Work and Poverty During Economic Restructuring:

Summaries Colombia escaped the worst of the debt crisis and has voluntarily adopted the kind of economic restructuring advocated by the World Bank and the IMF. Its experience represents a partial test of the effects of neo?liberal economic policy on the urban poor. Employment trends in Bogotá suggest that many of the fears about economic restructuring are unjustified. Despite liberalisation and a doubling in the numbers seeking work, unemployment rates have fallen. Jobs have been created, although principally in the informal sector. Feminisation has been operating very strongly in Bogotá and the sexual division of labour has begun to change. Since 1970 poverty in Bogotá has become both less common and less serious. If households are less poor, however, it is principally because more adults are working. Real personal incomes during the 1990s declined. If less people are hungry, every adult is also a great deal busier

Creative Worthwhile Interaction Design

Over the last two decades, creative, agile, lean and strategic design approaches have become increasingly prevalent in the development of interactive technologies, but tensions exist with longer established approaches such as human factors engineering and user-centered design. These tensions can be harnessed productively by first giving equal status in principle to creative, business and agile engineering practices, and then supporting this with flexible critical approaches and resources that can balance and integrate a range of multidisciplinary design practices

The 1985/1986 Amendments to the Comprehensive Environmental Response, Compensation, and Liability Act: A Background Paper

20 pages. Contains 2 attachments

The Heterogeneity, Distribution, and Environmental Associations of Borrelia burgdorferi Sensu Lato, the Agent of Lyme Borreliosis, in Scotland

Genospecies controls were obtained from the laboratory of Dr. Muriel Cornet at the Institut Pasteur, Paris. We thank Bob Furness for collecting ticks from passerine birds, Steph Vollmer for processing the samples from one site, E. Packer, A. Wiebe, J. Low, E. Stephen, and J. Arthur for help collecting ticks, Kenny Raey for laboratory assistance, and Jackie Potts for statistical advice. Marianne C. James was funded by a Biotechnology and Biological Sciences Research Council (BBSRC) Doctoral Training Grant with CASE support from the Macaulay Development Trust awarded to Alan S. Bowman and Lucy Gilbert. Lucy Gilbert was supported by the Scottish Government’s Rural and Environment Science and Analytical Services Division (RESAS).Peer reviewedPublisher PD

Medium optimization case study for continuous upstream process

Based on other mature industries, continuous upstream process is a logical replacement for current fed batch operations. However most industrial medium development has focused on the biological requirements for fed batch and therefore focused on the needs of stationary phase production. There is not an a priori expectation that growth and stationary phase requirements are identical. Yet an ideal continuous upstream process requires some combination of both. An optimal continuous upstream process requires a high cell density similar to fed batch operations. There is also some minimum growth rate required in order to match the combined death and cell removal rate at steady state. Hence, medium optimization yielding high productivity and sustaining sufficient growth is critical. In our work, we first established the minimum metabolic requirements to exceed high cell density at high viability based on our existing cell culture medium platform. Furthermore, the cells were able to reach a high cell density within only a few days post inoculation. Optimization was still required in order to shift from such a rapid growth process to a desirable high productivity continuous process. Fortunately, a continuous system is an ideal setup within which to evaluate multiple effects sequentially. An individual component can be spiked into the culture, and the direct impact can be monitored on cell growth and productivity. As the continuous system will continually wash out the component, the individual component impact is temporal and eventually the system returns to steady state in the absence of the spiked component. This process can be repeated iteratively until an optimal result is obtained. In our case, multiple positive effects were combined into one medium composition specifically optimized for a continuous upstream process